Three-dimensional mask simulations based on feature images

Abstract

A layout geometry of a lithographic mask is received. The layout geometry is partitioned into feature images, for example as selected from a library. The library contains predefined feature images and their corresponding precalculated mask 3D (M3D) filters. The M3D filter for a feature image represents the electromagnetic scattering effect of that feature image for a given source illumination. The mask function contribution from each of the feature images is calculated by convolving the feature image with its corresponding M3D filter. The mask function contributions are combined to determine a mask function for the lithographic mask illuminated by the source illumination.

What is claimed is: 
     
       1. A method comprising:
 receiving a layout geometry of a lithographic mask, wherein the layout geometry of the mask comprises a plurality of polygons; 
 partitioning the layout geometry into a plurality of feature images, wherein the feature images are images that represent geometric features present in the layout geometry of the lithographic mask and partitioning the layout geometry into feature images comprises rasterizing the mask polygons using a low-pass rasterization function that has a non-uniform response in a frequency passband; 
 calculating, by a processor, a mask function (MF) contribution from each of the plurality of feature images by convolving the feature image with a corresponding mask 3D (M3D) filter, wherein the M3D filter corresponding to a feature image represents an electromagnetic scattering effect of the geometric feature represented by that feature image and the M3D filters include effects of an equalization filter that compensate for the non-uniform response; and 
 combining the calculated MF contributions to determine a mask function for the lithographic mask. 
 
     
     
       2. The method of  claim 1  further comprising:
 determining the M3D filters by rigorous electromagnetic simulation of the scattering effects of mask structures based on the geometric features illuminated by a source illumination. 
 
     
     
       3. The method of  claim 1  wherein the plurality of feature images are selected from a library that contains predefined feature images and their corresponding precalculated M3D filters. 
     
     
       4. The method of  claim 3  wherein the library of predefined feature images comprises feature images of different order complexity, and the method further comprising:
 precalculating the M3D filters in an order according to their complexity. 
 
     
     
       5. The method of  claim 4  wherein determining the M3D filter for a feature image of higher order complexity comprises:
 determining a mask structure corresponding to the higher-order feature image; 
 partitioning the mask structure into the higher-order feature image and one or more lower-order feature images; 
 executing a rigorous electromagnetic simulation to predict a mask function for the mask structure; 
 calculating the MF contributions from each of the plurality of lower-order feature images by convolving the lower-order feature image with its corresponding M3D filter; and 
 determining the M3D filter for the higher-order feature image, based on combining the MF contribution from the higher-order feature image with the MF contributions from the lower-order feature images to yield the predicted mask function for the mask structure corresponding to the higher-order feature image. 
 
     
     
       6. The method of  claim 4  further comprising:
 determining the predefined feature images in the library, based on which geometric features are present in the layout geometry of the lithographic mask. 
 
     
     
       7. The method of  claim 6  wherein the library of predefined feature images comprises a common base of feature images supplemented by higher-order feature images for geometric features present in the layout geometry of the lithographic mask. 
     
     
       8. The method of  claim 1  wherein rasterizing the mask polygons produces grayscale feature images. 
     
     
       9. The method of  claim 1  further comprising:
 applying the mask function as input to an Abbe imaging model or Hopkins imaging model. 
 
     
     
       10. A system comprising:
 a computer readable storage medium storing instructions and a library containing predefined feature images and corresponding precalculated mask 3D (M3D) filters, wherein the predefined feature images are images that represent geometric features present in layout geometries of lithographic masks; and 
 a processor, coupled with the computer readable storage medium and to execute the instructions, the instructions when executed cause the processor to:
 partition a layout geometry of a lithographic mask into a plurality of feature images selected from the library; wherein the layout geometry of the mask comprises a plurality of polygons and partitioning the layout geometry into feature images comprises rasterizing the mask polygons using a low-pass rasterization function that has a non-uniform response in a frequency passband; 
 calculate mask function (MF) contributions from each of the plurality of feature images by convolving the feature image with the corresponding M3D filter from the library, wherein the M3D filters include effects of an equalization filter that compensate for the non-uniform response; and 
 combining the calculated MF contributions to determine a mask function for the lithographic mask. 
 
 
     
     
       11. The system of  claim 10  wherein the library of predefined feature images comprises an area image, one or more single-edge images, and multiple multi-edge images. 
     
     
       12. The system of  claim 11  wherein the library of predefined feature images comprises multiple feature images each consisting of two parallel edges. 
     
     
       13. The system of  claim 11  wherein the library of predefined feature images comprises multiple feature images each consisting of two perpendicular edges that form a corner. 
     
     
       14. The system of  claim 11  wherein the library of predefined feature images comprises multiple feature images each consisting of a single edge oriented at an angle that is not a multiple of 45 degrees. 
     
     
       15. The system of  claim 11  wherein the library of predefined feature images comprises multiple feature images each consisting of a curvilinear edge. 
     
     
       16. A non-transitory computer readable medium comprising stored instructions, which when executed by a processor, cause the processor to:
 partition a layout geometry of a lithographic mask into a plurality of feature images, wherein the feature images are images that represent geometric features present in the layout geometry of the lithographic mask, the layout geometry of the mask comprises a plurality of polygons, and partitioning the layout geometry into feature images comprises rasterizing the mask polygons using a low-pass rasterization function that has a non-uniform response in a frequency passband; 
 calculate a mask function (MF) contribution from each of the plurality of feature images using mask 3D (M3D) filters for the feature images, wherein the M3D filters include effects of an equalization filter that compensate for the non-uniform response; and 
 combine the calculated MF contributions to determine a mask function for the lithographic mask. 
 
     
     
       17. The non-transitory computer readable medium of  claim 16  wherein the M3D filters are based on rigorous electromagnetic simulation. 
     
     
       18. The non-transitory computer readable medium of  claim 16  wherein the layout geometry comprises a layout geometry for an entire chip. 
     
     
       19. The non-transitory computer readable medium of  claim 16  wherein a source illumination of the lithographic mask is an extreme ultraviolet (EUV) or deep ultraviolet (DUV) illumination.